Estimation Of The ARFIMA Parameters: A Comparison Study And Application In Financial Time Series

Long memory characterizes higher order correlation structures, also known as long-term dependence. The sequence with long memory has a stable dependence on the observed values between two values, and the slowly decaying autocorrelar tion function. The nonlinear characteristics of the fat tail of financial time series distribution, fractal structure, chaotic behavior and long-term memory, is one of the most important issues for years. In order to gain a deep understanding of the characteristics of long memory in economic time series, this paper focuses on the study of the model of the autoregressive fractionally integrated moving aver-age(ARFIMA) model. And we introduced the concept, testing and setting model of long memory time series. The ADF, PP, KPSS test are employed to examine the stability of the two series. Using classical R/S analysis, modified R/S analy-sis and V/S analysis, we detect long memory of daily return series of Shanghai and Shenzhen have obvious long memory. And the long memory of Shanghai is stronger than Shenzhen. Based on these results,we use the ARFIMA model with B-J to investigate the long memory of Shanghai and Shenzhen daily return series.It is confirmed by Information Cirterion that ARFIMA(6, d, 2) is the best model for Shanghai and ARFIMA(5, d, 2) is the best model for Shenzhen. Through em-pirical research, We consequently draw conclusion that there is a long memory in Chinese stock market, but the stock market is lack of effectiveness.